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Análise das características de ruído em séries temporais GPS
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A presença de ruído em séries temporais produz efeitos significativos sobre as incertezas das velocidades baseadas nessas séries e é, por isso, importante contabilizar o ruído existente numa série, de forma a avaliar a magnitude do seu efeito, relacionando as incertezas com as amplitudes de ruído. As séries temporais apresentam fontes de erros que evidenciam a presença de ruído branco juntamente com ruído colorido (temporalmente correlacionado).
Este estudo avaliou as características do ruído de um conjunto de 55 séries temporais de posições semanais estimadas a partir de dados obtidos com o Sistema de Posicionamento Global (GPS - Global Positioning System), de estações localizadas em Portugal e Espanha.
Para caracterizar o ruído presente nas séries temporais foram utilizados diversos modelos de ruído e combinações de modelos de ruído, que permitiram estudar e comparar os processos de ruído estocásticos em séries temporais contínuas, apontar qual o melhor modelo ou combinação que descreve o ruído presente nas séries observadas e simultaneamente determinar incertezas mais próximas da realidade para a velocidade da estação. As amplitudes de ruído das séries temporais obtidas para cada uma das componentes indicaram que a combinação de ruído branco com ruído rosa é a que melhor descreve o ruído presente na série, indicando que, em séries temporais de coordenadas GPS, o ruído branco não é dominante. Quando o índice espectral não é especificado, é necessário determinar o índice que minimiza o ruído para cada série. Verificou-se que os menores valores de ruído são estimados com os maiores índices espectrais e a média dos diversos índices espectrais calculados para as três componentes aponta o índice de -0.97 para alcançar o menor ruído.
Correlacionando as incertezas de velocidade obtidas pelo modelo de ruído branco e pela combinação de modelos de ruído branco com ruído rosa, foi possível determinar um factor que permite relacionar as incertezas das velocidades entre esses modelos. Nesse sentido, conclui-se que as incertezas baseadas num modelo de ruído branco com ruído rosa são cerca de 3.3 vezes superiores às obtidas com base num modelo de ruído branco.
The presence of noise in time series produces meaningful effects in the uncertainties of the velocities based on those series. Therefore, it is important to evaluate the noise in a series, in order to access the magnitude of its effect, and to relate the velocities uncertainties with the noise amplitudes. The time series presents error sources that show the presence of white noise with coloured noise (time correlated). In this dissertation, the noise characteristics of a set of 55 time series of weekly positions based on Global Positioning System (GPS) data for stations located in Portugal and in Spain are evaluated. To characterize the noise present in the time series were used several noise models and combinations of noise models that allowed to study and to compare the stochastic noise processes in continued time series, to indicate the best model or combination that describes the noise present in the observed series, and simultaneously to determinate the realistic uncertainties of the station velocity. The obtained noise amplitude of the time series for each of the components indicated that the combined white noise with flicker noise is the one that best describes the noise present in the series, indicating that the white noise is not dominant in GPS coordinate time series. When the spectral index is not specified, it is essential determinate the index that minimizes the noise for each time series. It was verified that lower values of noise are estimated with higher spectral index and the average of the several calculated spectral index to the three components, indicates the -0.97 rate to obtain the lower noise. Correlating the uncertainties of velocity obtained by the white noise and by the combined models of white noise and flicker noise, it was possible to establish a relation between the uncertainties of the velocity for the different models. Accordingly, it is concluded that the uncertainties of the velocities based on a combination of white noise and flicker noise are about 3.3 times higher than those based on white noise only.
The presence of noise in time series produces meaningful effects in the uncertainties of the velocities based on those series. Therefore, it is important to evaluate the noise in a series, in order to access the magnitude of its effect, and to relate the velocities uncertainties with the noise amplitudes. The time series presents error sources that show the presence of white noise with coloured noise (time correlated). In this dissertation, the noise characteristics of a set of 55 time series of weekly positions based on Global Positioning System (GPS) data for stations located in Portugal and in Spain are evaluated. To characterize the noise present in the time series were used several noise models and combinations of noise models that allowed to study and to compare the stochastic noise processes in continued time series, to indicate the best model or combination that describes the noise present in the observed series, and simultaneously to determinate the realistic uncertainties of the station velocity. The obtained noise amplitude of the time series for each of the components indicated that the combined white noise with flicker noise is the one that best describes the noise present in the series, indicating that the white noise is not dominant in GPS coordinate time series. When the spectral index is not specified, it is essential determinate the index that minimizes the noise for each time series. It was verified that lower values of noise are estimated with higher spectral index and the average of the several calculated spectral index to the three components, indicates the -0.97 rate to obtain the lower noise. Correlating the uncertainties of velocity obtained by the white noise and by the combined models of white noise and flicker noise, it was possible to establish a relation between the uncertainties of the velocity for the different models. Accordingly, it is concluded that the uncertainties of the velocities based on a combination of white noise and flicker noise are about 3.3 times higher than those based on white noise only.
Descrição
Tese de mestrado em Engenharia Geográfica, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2013
Palavras-chave
Séries temporais Ruído branco Ruído rosa Ruído vermelho Incertezas Teses de mestrado - 2013